Enemies with more combat actions and equal or higher weapon skills than your hero have advantage over him. But even lesser enemies can defeat the most skillful hero if there is horde of them. Then there are magical attacks etc. which can make the battlefield very dangerous place even for the most skilled hero.

Also remember that even if he parries he still suffers the effects of knockback from mighty blows. So even if your hero can parry the hits of the giant demon or dragon he could still get knocked prone and suffer damage from knockback (if the knockback pushes him over the edge of a cliff or something similar).

Also there are situations where wearing full plate is just stupid. Here are some examples: In some settings walking around the cities wearing full plate and carrying huge shield is a faux pas, especially in social gatherings. While it is possible that the assassins will attack to a banquet, normal people don't participate to such events wearing their battle gear. Wearing full metal armour can also be dangerous while on ship or when climbing in mountains. So either the player removes part of his heavy equipment or his character might end up suffering the ill effects of carrying too much metal.

During opposed tests, whichever participant has the highest mastered skill subtracts 100% from
it and uses the remainder as a penalty to everyone in the contest. Thus the most skilled participant
has a skill of 100% and everyone else is less than this. This has the benefit of introducing an
increased chance of failure for the lesser skilled opponents in the contest; thus improving the
chance of a better victory level.
For example, Mikhail the mercenary possesses a Stealth skill of 120%. Since he is the most experienced
character he reduces all his opponents’ Perception skills by 20% and he himself is lowered to 100%.
The identification of who has the highest skill must be calculated after any other modifiers for
circumstances have been applied"

Roleplay combat's not like chess. It's possible for him to play a defensive game, and still get chopped up by ranged attacks, attacks with a longer Reach to keep him at bay and back him into a corner where he cannot harm anybody, spells, fire - do you think Parry works well against Dragon's Breath or being smacked in the face by the burning end of a flaming torch or, I dunno, someone throwing lantern oil over his shield and then hitting it with fire from that torch? - or similar non-weapon attacks.

I actually use Runequest/Legend combat rules in a system that "borrowed" rules from many different games out there.
I have also borrowed some class-thinking, "rock-paper-scissors" from Dark age of Camelot.

And this particular player is playing a warrior-class, defence heavy with the ability to block incoming attacks against his "groupmembers", so I guess its alright the way it is, but I wanted to make him hurt from time to time, just so he realizes that he can be killed.

But magic, fire and ranged attacks to drain him of action points are all good ideas.